Multiscale Modeling of Three Dimensional Discrete Dislocation Dynamics and Boundary Element Method and Its Application to Nanoindentation Problem

Abstract

In the nano-plastic deformation, material properties such as yield stress cannot be described by the average rate of whole dislocation behavior, and it becomes increasingly necessary to trace individual motion of dislocations. The relationship between indent load-displacement in nanoindentation test is the typical example of recognizable nano-plasticity. Molecular dynamics (MD) is one of the most effective methodologies to obtain dislocation motion directly. However, MD simulation depends on the computer power so strongly that it is difficult to treat mesoscopic behavior including collective dislocation motion. On the other hand, discrete dislocation mechanics (DD) based on dislocation theory has a unique ability to treat dislocation motion, although boundary value problem in the DD framework would pose considerable difficulties. In the present paper, we construct a combined approach including both DD and the boundary element method (BEM), and succeed in representing the stress field of dislocation in the vicinity of traction free surface. Finally, we apply this model to the nanoindentation problem and found the relationship between displacement burst and collective dislocation motion.